Efficient Identification of Equivalences in Dynamic Graphs and Pedigree Structures

Executive Summary

The authors propose a new framework for designing test and query functions for complex structures that vary across a given parameter such as genetic marker position. The operations they are interested in include equality testing, set operations, isolating unique states, duplication counting, or finding equivalence classes under identifiability constraints. A motivating application is locating equivalence classes in Identity-By-Descent (IBD) graphs, graph structures in pedigree analysis that change over genetic marker location. The nodes of these graphs are unlabeled and identified only by their connecting edges, a constraint easily handled by their approach. The general framework introduced is powerful enough to build a range of testing functions for IBD graphs, dynamic populations, and other structures using a minimal set of operations.